Q 52. - Calculus

Question

Determine the domains of the functions in Exercises 47–56, and find where the functions are continuous.  

$f(x,y,z)=e^{-xyz}$

Step-by-Step Solution

Answer

The function $f(x,y,z)=e^{-xyz}$is continuous on $f^3$.

Step 1. Given information.

We have given expression: $f(x,y,z)=e^{-xyz}$

Step 2: To find continuous of the function.

The given function is

 $$\begin{gathered} f(x,y,z)=e^{-xyz} \\ =\frac{1}{e^{xyz}} \end{gathered}$$

The given function is reciprocal of exponential function. The domain of an exponential function is the entire set of real numbers.

Domain of $f$ is  $f^3 or \left\{\left(x,y,z\right):x,y,z\in f\right\}$

The exponential function is said to be continuous over its domain always.